Scalability remains a central challenge in large-scale quantum architectures. While device-level characterization is essential, many scalability constraints originate at the architectural level, where global coordination limits and asymptotic instabilities emerge prior to layout, compilation, or hardware modeling. We introduce a structural admissibility framework positioned as a pre-hardware diagnostic layer for architecture-level scalability assessment. Architectures are modeled as controlled scaling families, and admissibility is determined by a set of structural functionals governing growth consistency, compositional refinement, and perturbative stability. These functionalsestablish whether a family supports coherent large-scale expansion before physical realization. To obtain measurable diagnostics, each structural instance is associated with a symmetric operator from a minimally specified axiomatic class. The smallest non-zero eigenvalue defines a spectral gap observable whose scaling yields a coherence-like indicator, an effective structural dimension estimate, and a quantitative measure of scaling fragility. Baseline experiments using the normalized graph Laplacian show that purely structural observables already separate distinct scaling regimes—such as mediation-dominated 1D chains and dimension-supported 2D grids—without invoking device-level noise models.
Scalability remains a central challenge in large-scale quantum architectures. While device-level characterization is essential, many scalability constraints originate at the architectural level, where global coordination limits and asymptotic instabilities emerge prior to layout, compilation, or hardware modeling. We introduce a structural admissibility framework positioned as a pre-hardware diagnostic layer for architecture-level scalability assessment. Architectures are modeled as controlled scaling families, and admissibility is determined by a set of structural functionals governing growth consistency, compositional refinement, and perturbative stability. These functionalsestablish whether a family supports coherent large-scale expansion before physical realization. To obtain measurable diagnostics, each structural instance is associated with a symmetric operator from a minimally specified axiomatic class. The smallest non-zero eigenvalue defines a spectral gap observable whose scaling yields a coherence-like indicator, an effective structural dimension estimate, and a quantitative measure of scaling fragility. Baseline experiments using the normalized graph Laplacian show that purely structural observables already separate distinct scaling regimes—such as mediation-dominated 1D chains and dimension-supported 2D grids—without invoking device-level noise models.
Scalable quantum architectures are increasingly constrained by mesoscopic structural effects that emerge prior to hardware realization. While a foundational admissibility layer establishes spectral consistency of scaling families, admissibility alone doesnot ensure favorable physical scaling behavior as architectures grow. This work introduces a second diagnostic layer aimed at quantifying architecture-level structural risk under controlled growth. Assuming admissibility has been verified, we analyze parametrized architectural graph families and extract a minimal set of physically interpretable observables derived from a symmetric structural operator. By examining the scaling of load concentration, mediation overhead, and perturbationinduced amplification, we estimate global and local growth exponents and define a Relative Structural Risk Index (SRI) for comparative assessment across architectures. The framework is evaluated on multiple architectural families, including linear chains, planar grids, centralized star topologies, modular hierarchical constructions, and a constraintmediated architecture inspired by parity-based encodings. The results indicate that spectrally admissible architectures can nonetheless exhibit substantially different mesoscopic scaling regimes. The proposed diagnostic layer functions as a pre-hardware structural assessment instrument, supporting architecture-level decisions prior to layout optimization, hardware prototyping, or error-correction design.
Efforts to scale quantum hardware are commonly framed as a challenge of suppressing local decoherence and stochastic noise through improved physical qubits and quantum error correction. Yet large-scale devices routinely exhibit performance degradation inconsistent with bounded-complexity local noise models, including nonstationary drift, bursty correlated events, and long-range crosstalk. We propose a constraint-based scaling framework in which the dominant limitation to scalability is not local error amplitude but the accumulation of constraint geometry: structured, correlated degrees of freedom that grow with system size and cannot be absorbed by standard endogenous noise models. We formalize this via (i) a bounded-complexity endogenous model class, (ii) a structured residual observable isolating unexplained degradation, and (iii) a coherence budget comparing effective control capacity to constraint burden. We identify a regime transition-the coherence wall-at which constraint burden outpaces control capacity, leading to rapid performance collapse despite stable local fidelities. We provide operational measurement protocols for extracting structured residual scaling, correlated dimensionality, and perturbation sensitivity from standard benchmarking data. The framework yields falsifiable architectural predictions and offers a diagnostic layer bridging quantum theory and scalable quantum engineering.
This paper develops an engineering-facing diagnostic bridge between the recoverability-based theory of structural irreversibility and practical evaluation in quantum error correction and monitored quantum platforms. The central problem addressed in this work is that structural recoverability, threshold-like margins, false-collapse, and Recoverability Index–type diagnostics provide useful theoretical distinctions, but they do not by themselves specify how experimentalists or engineers should organize platform-level data, compare regimes, or report recoverability-relevant behavior. The paper therefore introduces a proxy map from structural quantities to engineering diagnostics. Generalized recoverability is associated with recovery performance, decoder-assisted restoration, logical-state fidelity, and related reconstruction-sensitive quantities. Threshold-like margins are associated with entropy-like, noise-sensitive, or transition-localizing proxies. False-collapse is associated with mismatch windows in which collapse-like or transition-like indicators become strong while recovery-sensitive records still indicate residual recoverability. The paper also proposes a minimal diagnostic architecture for QEC and monitored platforms. This architecture consists of four layers: an appearance-sensitive proxy, a recoverability-sensitive proxy, a threshold-like locator, and a window-based reporting layer. Together, these layers support regime classification, early-warning detection, false-collapse-like mismatch identification, finite-window reporting, and cross-regime comparison. A QEC-oriented realization is presented to show how syndrome histories, logical-failure markers, logical recovery performance, entropy-like proxies, false-collapse window frequencies, and RI-like summaries can be organized into a coherent diagnostic workflow. The goal is not to replace detailed decoder analysis or hardware-specific benchmarking, but to provide a bridge-level language for deciding what should be logged, estimated, compared, and reported when studying the approach to effective irreversibility in error-managed quantum systems. This work should be read as an engineering and experimental companion to the broader recoverability program. Its contribution is to make structural irreversibility operationally legible by mapping theoretical quantities to measurable, computable, and reportable diagnostics in contemporary quantum platforms.
We develop a mathematically rigorous and experimentally testable framework for the classification of physical regimes based on the modular structure of quantum states. The central object of the theory is the modular generator K = −log ρ, which provides a unified language for spectral, geometric, and information-theoretic diagnostics. We introduce a universal instrument panel (MSRO: Modular–Spectral RG Observables) that integrates spectral quantiles, commutator-based response functions, partition-based locality diagnostics, and information-geometric structures. A key requirement of the framework is strong portability: the same diagnostic protocol applies across multiple domains—including open quantum systems, information geometry, entanglement-based models, and RG-like flows—without domain-specific retuning. The main result of the work is the derivation of a universal and experimentally testable scaling law for the modular response signal: ν(λ) ∼ 1 log λ, which characterizes critical regimes in a wide class of quantum systems. We prove that this scaling emerges from spectral asymptotics of the modular operator and establish a strict equivalence between spectral, geometric, and information-theoretic descriptions of criticality: ν ↔ k(q) ↔ I(λ) ↔ K ↔ R ↔ Δ. The framework is supported by functional analytic results (including Fr´echet differentiability of log ρ), operator inequalities (Golden–Thompson, monotonicity of relative entropy), and stability estimates. We further provide a concrete experimental protocol for quantum simulators, including statistical error bounds and Fisher information constraints, making the prediction directly testable. Beyond regime classification, the results suggest a new perspective on criticality as a geometric phenomenon associated with vanishing modular curvature. The approach opens pathways toward large-N limits, quantum field extensions, and the discovery of new classes of non-standard critical behavior.
We identify minimal structural requirements that any physical description must sat- isfy to represent persistent, coherent systems capable of internal dynamics. Rather than postulating new dynamical laws, we work at an architectural level, isolating constraints implied by the empirical fact that localized entities endure, remain measurable, and support stable internal motion. The first constraint is closure: coherence must be selec- tively retained rather than dispersed, which enforces an admissible boundary (physical or effective) and thereby supports resonance. In bounded or effectively bounded sectors, closure produces isolated spectral features—eigenmodes or long-lived quasi-modes—that render coherent configurations countable and stable. Spectral stability in turn requires self-adjoint operator structure so that observables remain real and evolution is norm- preserving. Finally, coherent internal motion requires a complementary skew-adjoint circulation/transport component, compatible with the stable spectral backbone but capable of generating nontrivial flow. These elements assemble into a unified operator architecture with three roles: admissibility (domain and boundary), closure/stability (self-adjoint spectral structure), and circulation/transport (skew-adjoint motion). The framework clarifies a common structural spine underlying quantum theory, field the- ory, and geometric constraint, while remaining agnostic about specific microscopic realizations.
Eigenstate Engineering as Admissibility Architecture: Constraint-History Retention, Recursive Eigenspace Sculpting, and the Experimental Emergence of Persistent Quantum Accessibility This work introduces Eigenstate Engineering as Admissibility Architecture (EEAA), an admissibility-first framework for understanding how recursively structured quantum interactions reshape the practical accessibility of eigenstate manifolds under standard quantum mechanics. Rather than treating eigenstates solely as static operator solutions, the paper proposes that bounded, path-dependent, non-commuting control sequences can bias future coherent reachability by sculpting admissible eigenspace accessibility over time. Anchored in orthodox Hamiltonian dynamics, Floquet engineering, decoherence theory, and coherent control, the framework introduces no new particles, forces, or departures from established physics. Instead, it reorganizes known quantum formalisms under an admissibility-first interpretation in which persistence, orderability, and bounded continuation govern experimentally realizable state accessibility. The paper formalizes operators and diagnostics for: admissible eigenspace deformation, history-retentive accessibility, potency-conditioned state volume, recursive control sequencing, and constraint-history retention in coherent quantum systems. A central empirical motivation is the recent trapped-ion quadsqueezing breakthrough achieved through staged non-commuting interactions, demonstrating that recursively admissible sequencing can unlock higher-order eigensectors dramatically faster than conventional direct-driving approaches. The work interprets such results as evidence that practical eigenspace accessibility can be systematically reshaped through bounded interaction history. The EEAA framework further develops falsifiable predictions across: trapped-ion systems, superconducting qubits, Floquet-engineered lattices, topological materials, quantum sensing architectures, and coherent quantum memory systems. Conceptually, the work extends a broader admissibility-first research program in which persistence under constraint, orderability, and bounded continuation are treated as minimal structural preconditions for experimentally resolvable physical systems. Related foundations include admissible continuation geometry, recursive accessibility deformation, χ-based stability diagnostics, potency-conditioned continuation volume, and deterministic boundary projection under exhausted admissible continuation. The paper is intended as a falsifiable interpretive and engineering framework for coherent quantum accessibility rather than a replacement for standard quantum mechanics. Its central claim is operational: recursively staged admissible control sequences can sculpt the practical geometry of eigenstate accessibility and thereby function as effectively programmable accessibility structures for persistent coherent quantum behavior. All claims are formulated within experimentally testable control-theoretic and dynamical regimes compatible with standard quantum mechanics. Keywords Quantum Physics Quantum Mechanics; Eigenstate Engineering; Quantum Control; Coherent Control; Quantum Accessibility; Quantum Memory; Trapped Ions; Quadsqueezing; Floquet Engineering; Quantum Dynamics; Quantum Information; Quantum Architecture; Hamiltonian Dynamics; Non-Commuting Operators; Eigenspace Accessibility; Quantum State Accessibility; Coherent State Reachability Admissibility-First Framework Admissibility Architecture; Admissible Continuation; Constraint-First Physics; Constraint-History Retention; Recursive Accessibility; Bounded Continuation; Persistence Under Constraint; Orderability; Potency; χ-Diagnostics; Boundary Projection; Recursive Eigenspace Sculpting Mathematical / Theoretical Physics State-Space Geometry; Accessibility Manifolds; Operator Theory; Stability Geometry; Constraint Topology; Recursive State Reachability; Nonlinear Quantum Accessibility; Phase-Space Structure; Dynamical Constraints; Admissible Projection Operators; Quantum Control Geometry Experimental / Applied Systems Superconducting Qubits; Quantum Sensing; Topological Quantum Systems; Coherent State Engineering; Quantum Hardware Architecture; Experimental Quantum Control; Recursive Control Sequences; Higher-Order Squeezing; Quantum Coherence Engineering Philosophy / Foundations of Physics Interpretations of Quantum Mechanics; Emergent Accessibility; Constraint Geometry; Physical Continuation; Geometry of Quantum Reachability